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Compressible and Choked Flows in Rotating Passages

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DOI: 10.4236/ojfd.2019.91001    204 Downloads   358 Views Citations

ABSTRACT

The present study revisits the rotating duct problem examined by Polihronov and Straatman (J. Polihronov and A. G. Straatman, Phys. Rev. Lett. v. 109, p. 054504 (2012)). Starting from the general compressible Euler equations in a non-stationary reference frame closed form expressions for velocity, temperature, density and pressure along the duct are determined. The present results are more general than those obtained by Polihronov and Straatman, as the change of in-frame kinetic energy has been retained. The improvement of the present results over Polihronov and Straatman’s is demonstrated by comparison with the results of a computational fluid dynamics study. The new results have been further generalized to the case of a rotating duct with varying cross-sectional area, and again for a general curved passage in three-dimensional space. The work required or derived from the rotating duct has also been computed. The choked flow condition within the passage of varying cross-sectional area has been identified, along with the constraints which must be placed on the Mach, Rossby, and tip Mach numbers to avoid choked flow. Finally, a straightforward technique to identify any locations where an ideal rotating flow in a constrained passage will become sonic has been presented.

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Dyck, N. and Straatman, A. (2019) Compressible and Choked Flows in Rotating Passages. Open Journal of Fluid Dynamics, 9, 1-21. doi: 10.4236/ojfd.2019.91001.

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